“10 years on average doesn’t mean 10 years in any case” — an Experimental
Investigation of People’s Understanding of Fixed and Continuous Delays
Andreas Grofler”, Inge Bleijenbergh’, Jac Vennix!
Submission to
International System Dynamics Conference 2011, Washington
May 2011
1 Institute for Management Research, Radboud University Nijmegen, P.O. box 9108, 6500
HK Nijmegen, The Netherlands
* corresponding author: a.groessler@ fm.ru.nl, +31 24 36 16287, +31 24 36 11933
“410 years on average doesn’t mean 10 years in any case” — an Experimental
Investigation of People’s Understanding of Fixed and Continuous Delays
Abstract
The purpose of the paper is to test whether people make different decisions when a dynamic
task requires either a fixed delay or a continuous delay representation. We assume that
people have a tendency to cognitively represent continuous delays in real life situations as
fixed delays. With the help of a structurally simple dynamic decision making task, we test two
conditions in a controlled experiment: hiring when personnel stays in an organisation for
exactly ten years (fixed delay condition) or when personnel stays on average for ten years
(continuous delay condition). In this preliminary study, 71 participants were tested. Findings
so far show no differences in performance between the groups, indicating that they most likely
use the same cognitive representation of the task. Since participants’ answers are
substantially closer to the fixed delay condition, we assume that people have the tendency to
represent lags in the form of discrete delays, at least in the context of personnel hiring.
Research implications comprise the repetition of the experiment to achieve a higher number
of participants and to allow for a more extreme differentiation between the two conditions.
Practical implications regard the formulation of decision making tasks within organisations,
for instance in human resource management. The value of this paper lies in its rigorous usage
of a structurally simple dynamic task to shed light on a fundamental trait of human decision
making.
Keywords: discrete delay, continuous delay, experiment, personnel hiring, female professors
task
1 Introduction: Discrete and continuous delays
In this paper, we investigate how people make decisions that involve different forms of delays
in dynamic systems, and in personnel hiring in particular. Human resource managers are well
aware of the fact that hiring personnel involves a delay since not all personnel requirements of
organisations can be fulfilled instantaneously. However, what exact form they consider this
delay to have seems to be less clear. Earlier studies suggest that people have a tendency to
treat personnel hiring as a fixed delay, while in reality this process takes the shape of a
continuous delay (Grossler and Zock, 2010, Bleijenbergh et al., 2011). In this paper we test
this assumption. Due to the aggregate character of most system dynamics models, continuous
delays are more common in this field; however, in particular for technical processes, discrete
delays are used as well occasionally. In a stylized fashion, Figure 1 shows two delayed
response patterns to a system change, which are based on the two forms of delays used in this
paper (for comparison, a immediate response is shown as well, which is an example of non-
delay).
Input —-—-——-—— System response
x x x
a ==
! -T
I ¢
' ~
1
1 i
—— > >
ty t* t to t t
a) immediate b) discrete c) continuous
response delay delay
Figure 1: Forms of delays investigated in this paper (part a: non-delay response as comparison)
As can be seen in Figure 1, delays are characterised by two features: delay length and
delay order. Delay length (or delay time) signifies the time that elapses from the occurrence of
an input until a system response occurs. For reasons of clarification, part a) in Figure 1 shows
anon-delayed response of a system to an input, thus delay time is zero. In part b) of Figure 1,
delay time is the time from ty to t*; at time t* the total system response takes place. In the
continuous delay in part c), delay time is the time from ty until an average response occurs (at
time t*). Delay order signifies the shape of the system response. In a discrete delay, order is
infinite, leading to a full system response exactly when delay time has elapsed (part b) in
Figure 1). With continuous delay orders, system response becomes more gradual. This can
vary between a pronounced peak and a moderate curve. In the extreme case of a first-order
delay, an asymptotic response to an input occurs (part c) in Figure 1).
Figure 2 depicts the response of continuous delays of different order to a pulse input.
The figure shows graphically, how higher order continuous delays more and more resemble a
discrete delay (which is an infinite-order continuous delay). For further technical treatments
of delays see Forrester (1961, app. H), Rahn (1976) and Roy (2000).
Pulse input := 10; Delay time := 6
10 SJ
15
0 3 10 15 20 25 30 35 40 45 50
Time (months)
rate:120
rate:60
rate-30
Delay order: rate:10
rate:3
rate:1
Figure 2: Response of different order delays to pulse input
The purpose of the paper is to examine how people cognitively represent delays when
they perform a dynamic task, in order to contribute to improving decision making. By testing
whether people make different decisions when a dynamic task requires either a fixed or a
continuous delay representation, we examine the role of basic assumptions in this decision
making. With the help of a structurally simple dynamic decision making task (‘female
professors task’), we test the two delay forms as two conditions in a controlled experiment:
hiring when personnel stays in an organisation for exactly ten years (fixed delay condition) or
when personnel stays on average for ten years (continuous delay condition).
The motivation for this study stems from two observations. First, in an earlier
experiment we used the ‘female professors task’ (including a continuous delay formulation) to
investigate participants’ ability to understand and control this system (Bleijenbergh et al.,
2011). We wanted to know whether people were able to make a realistic estimation of the
personnel hiring to reach target figures. One outcome of the analyses of this case was that
participants in general underestimate the amount of personnel that need to be hired to reach a
target figure. A second outcome was that participants seemed to underestimate the delay
involved in reaching target figures. The results suggested that people cognitively represent
these delays as discrete, even when the task assumes a continuous delay, which would explain
their apparently sub-optimal performance in the task.
Second, in an extensive modelling and simulation project within a service organisation,
Grofler and Zock (2010) found that human resource management was severely hampered by
a mis-conception of the order of the delays involved. For the hiring process of employees,
human resource managers knew that it took on average 51 months until a new contracted
employee would be fully productive (they even used the words “on average”). However, they
interpreted it in a way that after 51 months all new employees would be available. Thus, they
understood a process that could be characterised by a continuous delay (with employees
needing less or more time than 51 months) as being a discrete delay (with all employees
needing exactly the same time of 51 months). Based on these two observations, we want to
shed some more light on cognitive representation of delays and their effect on managing
dynamic systems, in particular personnel hiring.
The structure of this paper is as follows. In the next section, we review the literature
conceming the effects of delays on decision making in dynamic tasks. We concentrate on
studies from the fields of system dynamics and complex problem solving in psychology. The
third section starts with a formulation of our research propositions. We continue with
describing the ‘female professors task’ and the actual experiment conducted, including the
characteristics of our research participants. In the fourth section, preliminary findings of the
experiment are presented. The paper closes with a discussion of findings, some preliminary
conclusions, and potential implications for research and practice.
2. Background: Existing research regarding the effects of delays on control
performance
Relevant studies regarding the effect of delays in decision making can be found in the system
dynamics as well as in the psychological literature on complex problem solving. We review
these literatures here, starting with two remarks. First, most studies do not explicitly address
the difference between discrete and continuous delays (thus, the order of the delays) and
rather focus on the length of the delay. Second, we do not include studies on the
understanding of accumulation processes or feedback loops here although they are necessarily
related (delays usually work in feedback loops; structurally, delays contain an accumulation
process). We refer to some more salient articles in this areas (accumulation: Booth Sweeny
and Sterman, 2000; Ossimitz, 2002; Sterman and Booth Sweeny, 2002; Pala and Vennix,
2005; Cronin et al., 2009; Sterman, 2010; feedback loops: Sterman, 1989; Diehl and Sterman,
1995; Langley et al., 1998).
In their review on dynamic decision making experiments in system dynamics, Rouwette
et al. (2004) identify “delays” as a characteristic that influences participants’ performance
when working with a system (e.g. in a dynamic task). They found four studies that
systematically investigate the effect of delays on decision making. The study by Sterman
(1989) does not vary delay time or order as such but uses it as an explanation for participants’
performance. Diehl and Sterman (1995) and Diehl (1989) vary the delay time and found
(partially mixed) results that indicate a decrease in performance with growing delay time.
Barlas and Ozevin (2001; updated and elaborated in Barlas and Ozevin, 2004) is to our
knowledge the only study that varies delay order (discrete vs. first-order continuous) in the
inflow to a production/inventory system. Their main finding is that fixed delays make a
system more oscillatory/unstable; continuous delays smooth participants’ reactions to external
inputs.
Rahmandad (2008) and Rahmandad et al. (2009) use simulations as experiments to
analyse the effect of delay time on organisational decision-making. They propose heuristics
with different qualities regarding decision-making under the influence of delays. Partially,
these two studies build on Repenning and Sterman (2002), in which the authors—based on a
case study—identify delays between investment in improvement programmes and the benefits
stemming from such programmes as being a major factor for misunderstanding the dynamics
of improvement initiatives. Like in most other studies, Repenning and Sterman discuss the
length of the delays as being critical. On the bases of simulation models, Yasarcan and Barlas
(2005) show that material delays, information delays, and secondary control of a stock can
5
result in similar behaviour pattems (in particular, oscillations); the authors propose the idea of
a “virtual supply line” and a general control heuristic suitable for all three forms of delayed
systems. Yasarcan (2011) reports on the effect of measurement delays (again referring to delay
length) on stock management performance and bases his investigation on simulation studies.
In the psychological literature on decision-making in complex situations (Stemberg and
Frensch, 1991; Brehmer and Domer, 1993; Frensch and Funke, 1995), quite some studies
vary the length of delays in systems as experimental input (we did not identify studies that
vary delay order). In many cases, delays are implemented in the experimental tasks in form of
information that is reported to participants with a time lag. Notable in this respect are the
studies by Brehmer (1989; 1990; 1992; 1995; Brehmer and Allard, 1991), mostly employing
his so-called ‘fire fighting task’. For instance, Brehmer (1995) reports on four experiments
with this task that vary delays on three different levels (reaction time of fire fighting crews,
response time of fire on fire fighting, reporting time of fire fighting success to headquarters).
One important finding from this study is that participants do not adjust their decisions
regarding systems control when delays are present compared to when there are no delays—
even when they got explicit information on the existence of these delays. Other psychological
studies employing delays as research objects are Mattern (1979), Funke (1985) and Reichert
and Domer (1988). All the psychological studies reviewed here use discrete delays in the
experimental tasks.
In summary, delays are acknowledged as a constituting element of dynamic decision
making and, thus, are the object of some studies in system dynamics and complex problem
solving that test their effect on participants’ performance. However, these studies (with one
exception) vary either delay time or whether there is a delay or not. Therefore, we identify
delay order (and its interpretation by humans) as a research gap to which our paper wants to
contribute, in order to improve our understanding of decision-making on dynamic tasks.
3. Experimental method
a. Propositions
Based on the two observations that built the motivation for this study (reported in Section 1)
and on the literature reviewed above, the following three research propositions were
formulated:
P1. People underestimate the effect of delays on the behaviour of systems.
P2. People’s decisions in a task that requires a discrete conceptualisation of delays
cannot be distinguished from people’s decisions in a task that requires a
continuous conceptualisation of delays.
P3. People cognitively represent delays in complex dynamic systems rather as
discrete delays than as continuous delays.
These propositions are investigated using a dynamic task (‘female professors task’) in a
controlled experimental setting.
b. Female professors task
The ‘female professors task’ that we use for our experiment focuses on a social issue in
human resource management, i.e. the gender (in)equality in higher management, more
specifically the issue of target figures to increase the number of women in top positions, and
in leading positions at universities in particular (Bleijenbergh et al., 2011; Bleijenbergh et al.,
2008). In a preceding experiment, this task was used in an attempt to find out to what extent
people understand the dynamic structure underlying changes in personnel composition and the
consequences for decision making on gender quota. Participants were told that the executive
board of a university has decided to close the gender gap of their university and to set a
gender balance (50/50 male and female full professors) as a target. Participants read a one
page description that: in the current situation there were 300 positions available of which 33
were filled by women and 267 by men; the number of positions was to remain unchanged for
the years ahead; the board had recently decided to start working with hiring quota to ascertain
that a gender balance, would be accomplished in the future. Participants were put in the
position of an advisor to this board and were given two questions:
ip What annual percentage of female professors would you recommend to hire as of
2010, given the target of gender balance?
ii. How much time does it take to realize the target of gender balance, given your
recommendation of an annual percentage?!
Next, they were asked to explain why they had chosen this percentage and target year (see
Appendix for original tasks handed out to participants). The task took around twenty minutes
for participants to accomplish.
The stock-and-flow structure of the task can be modelled as in Figure 3. Of course, this
simple structure embodies some assumptions. For instance, it is assumed that one person fills
one position (i.e. no part-time work), that all leaving professors are immediately replaced, and
* Please note that it was neither an explicit nor an implicit task to achieve the goal as fast as possible.
that all hirings, which are not in the recommended percentage of female professors, are male
professors. However, all these assumptions are consistent with the task.
Male professors
hiring males leaving males
percentage females _—— time at university hirings necessary
‘ng females Female professors
Figure 3: Stock and flow structure of ‘female professors task'
Rather than focusing on the relationship between the behaviour of a stock and a flow, or
controlling a manufacturing system, the ‘female professors task’ asks participants how to
balance two different stocks, given an initially unbalanced personnel situation. The first part
of the task (recommending the percentage) appears to be easy in the sense that, in order to
reach the target, the lower boundary is 50% and each recommendation equal or greater than
50% leads to goal achievement. Figure4 shows simulation results for four different
recommendations: 25%, 50%, 75%, and 100% hiring of female professors, in case of a
continuous third-order delay. As already implied, with a recommendation of 25% of women
to be hired, the target of an equal number of professor positions filled with women will never
be reached. With hiring 50% women, the goal will be reached eventually. Maintaining higher
percentages of women to be hired will result in more women than men being professor.
400
0 10 20 30 40 50 60 70 80 90 100
Female professors : Cont25. —4 4 4 4 4 4 4 4
Female professors : Cont50 2
Female professors : Cont75
Female professors : Cont100
Figure 4: Simulation results for different percentages of women hired, 3" order delay
The second part of the task (i.e. estimating the time frame to reach an equal gender
balance) is more complicated because participants have to take into account the dynamics of
the growth path. In our experiment for instance, female professors who are hired at a certain
point in time also leave/resign/retire, slowing down the increase of the proportion of female
faculty. As a result, reaching the target will take longer than might be expected.
c. Description of experiment and participants
In the experiment, two versions of the female professors task were used, representing the two
experimental conditions. The two versions differed only regarding three sentences (for the full
version see appendix). In the discrete delay condition the passage about the employment time
of professors reads:
“As a simplification, we assume that a full professor position is held for exactly
10 years (thus, all professors stay exactly the same period of time). After this
period, the professor retires or accepts a position at another university, so a new
professor can be appointed at that position.”
The continuous delay version is formulated as follows:
“On average, a full professor position is held for 10 years. This means that
some professors may stay for only a couple of years and then move on to
another university, while others may stay at this university for the rest of
their career. From the available data one can however conclude that the
average length of stay of a full professor is 10 years. Only after a professor
leaves, a new professor can be appointed at that position.”
The two versions of the female professors task were randomly distributed to the participants,
in order to get two experimental groups.
The experiment was conducted with a group of students at a Dutch university. All
students followed a course on Research Methodology as part of a special pre-master teaching
program to prepare them for a Master program in Business Administration. All students had
completed a Bachelor study before, including courses on Human Resource Management and
statistics. Thus, we consider them to have a basic idea about personnel issues and at least
rudimentary mathematical skills.
The participants answered the questionnaire (including open questions) in English
although English was not their native language. Not all participants answered the questions
completely. The information on sex, age or recommended percentage is missing for some
participants. We decided to exclude those participants from further analyses; of the original
79 participants, eight were excluded. The most important characteristics of the remaining 71
participants are presented in Table 1.
Table 1: Characteristics for all participants and the two experimental groups
Total Exp. group 1 Exp. group 2
@=712) Discretedelay Continuous delay
(@=36) (=35)
Age (x) 23.5 23.3 23.7
Sex (%)
Female 22.5 19.4 25.7
Male 77.5 80.6 84.3
Experimental groups can be assumed equal concerning average age and distribution of sexes.
In order to evaluate participants’ performance, the potential effects of their decisions
were tested with the help of a simulation model of the task (listings in the appendix). More
concretely, it was tested whether and when participants’ decisions would lead to target
achievement, i.e. a 50% ratio of female professors. The decisions of the discrete delay group
were compared with a discrete delay version of the model; the continuous delay group was
compared with an continuous delay version of the model.
10
4, Preliminary results of experiment
We discuss the results of our experiment in order of the three propositions formulated above.
a. Estimation of effects of delays (P1)
For the total group, the mean recommendation for a hiring quota for women is 54.2%.
However, a surprising 29.6% of participants (21 in absolute terms) give a recommendation of
hiring less than 50% female professors. With such a recommendation, the university’s target
of an equal gender balance never be reached. Furthermore, two participants recommend hiring
more than 100% women which is inconsistent with the task (and difficult to interpret). On
average, this performance is in line with the performance of participants in an earlier
experimental study employing the ‘female professors task’ (Bleijenbergh et al., 2011). In that
study, a substantially bigger share of participants was women than men. Thus, we could
replicate the experiment with a group of participants, which is mostly male and not female as
in the earlier study.
The estimations conceming the time it takes before the target would be achieved vary
between two and 57 years for the total group. The deviation of their estimation from the
correct target year—calculated using the respective simulation model—is on average 11.5
years (only calculated for those who give a reasonable percentage recommendation between
50% and 100%). When controlling for under- or over-estimation of the time needed to
achieve the target of 50% female professors, results show that on average the time necessary
is under-estimated (by 9.3 years), i.e. participants assume that the target can be reached faster
than actually is the case (with an extreme value of an under-estimation of 37 years). Nine
participants (roughly 12%) were correct with their estimate.
The scatter plot in Figure 5 summarizes the findings for the total group of participants
with reasonable recommendations. It demonstrates that in particular participants with a
relatively modest recommendation (at or only slightly above 50%) deviate in their estimate
from the correct value. It also shows that more participants under-estimate the time it takes to
achieve the targets (dots above zero line) than overestimate it (dots below zero line).
11
404
000
;
lo
:
®
'o
Deviation in years from correct estimate
T
°
ni
°
T 1 1 T 1 i
50.00 60.00 70.00 80.00 90.00 100.00
Percentage female appointments
Figure 5: Scatter plot for all participants relating recommendation in percentage of women hired and
deviation in estimation from correct value of target achievement
As a result concerning Proposition 1, we conclude that one third of the participants gave
a recommendation that would not lead to reaching the target. Roughly another third of the
participants wrongly estimates the time of reaching the target with an error of five years or
more. The last third gives a valid recommendation and their estimate shows an error of less
than five years. We interpret these findings to corroborate the results from earlier studies as
well as preceding experiments with the specific task: people have difficulties in understanding
the nature of accumulation and delays.
b. Comparison between discrete and continuous delay group (P 2)
When comparing the recommendations and estimations given in the two experimental groups,
we find no differences between those groups despite the different formulation about the order
of the delays in their tasks. On average, participants in the discrete delay condition
recommend to hire a slightly higher percentage of female professors than their counterparts in
the continuous delay condition (56.5% vs. 52.4%). Analogously, the discrete delay group
estimates to achieve the target a bit earlier than the continuous delay group (in 9.2 years vs.
10.8 years). However, these differences are statistically not significant. Table 2 shows the
results of a t-test with the discrete vs. continuous delay condition as the controlling variable.
12
Table 2: Results of t-tests to check for differences between experimental groups: recommendations
and estimations
Levene's Test for
Equality of Variances ttest for Equality of Means
Sig. (2- Mean
F Sig. t df tailed) Difference
Percentage women = Equal variances
appointed ascumed 1,302 .258 | .611 70 543 4.08083
Equal variances
notassumed .611 | 67.453 543 4.08083
Target achievement Equal variances
in assumed 336 564 | 886 68 379 “1.571
Equal variances
notagsumed .886 | 51.907 380 “1.571
Thus, with regard to Proposition 2 we conclude that indeed participants’ decisions are
not different for the two experimental conditions. Assumingly, no matter what the formulation
of the task is, they use the same kind of cognitive representation of delay in their decision
making on a hiring percentage and their estimation of the time it takes to reach the target.
c. Comparison of group results to simulated results (P 3)
While participants’ decisions are comparable despite the two different conditions, their
performance might be different in relation to the content of the task, i.e. whether they have to
deal with a discrete or with a continuous delay. For this reason we tested for differences in the
absolute deviation of their estimation of the target year with the actual target year (given their
individual recommendation). To do this, a simulation model of the condition was run,
parameterised with the different recommendations. In the discrete delay version, for instance,
it takes ten years to achieve a gender balance, in case 50% female professors are hired; in the
continuous delay version, it would take about 45 years with the same hiring percentage.” In
other words, while the participants use a comparable cognitive representation of the delay
involved, the actual situations the two tasks refer to, are very different in terms of the orders
of the delay of the effect of hiring percentages .
When comparing the goodness of the estimations between the two groups, differences
between the experimental conditions become obvious. On average, participants in the discrete
delay group wrongly over-estimate the time it takes to achieve the target by a mere 1.1 years.
However, the continuous delay group under-estimates it by 21.6 years on average. Needless to
* Technically, after this period the difference between the number of female and male professors is below two,
which we defined as goal achievement (since for continuous delays, the numbers in the 50% case are
approaching each other but a small rest remains).
13
say, differences between the groups concerning the absolute deviations are statistically
significant, as the t-test reported in Table 3 shows.
Table 3: Results of t-tests to check for differences between experimental groups: estimation against
actual target achievement—first-order delay system in continuous condition
Levene's Test for
Equality of Variances
t-test for Equality of Means
Sig. (2- Mean
F Sig. t df tailed) Difference
ABSDeviation Equal variances
CorrectEstima assumed 171.110 000 -5.822 45 000 -18.825
te
Equal variances
not assumed -5.500 23.596 000 -18.825
Since a first-order delay is the most “extreme” form of a continuous delay, we also
calculated the performance of the participants in the continuous delay group against the
results when a third-order delay is assumed to exist in the system.? In this case, it takes
roughly 25 years until a gender balance is achieved, when 50% female professors are hired in
each year. Table 4 shows the results of a t-test comparing the discrete group against the
continuous group, when its performance is evaluated relative to a third-order delay system. As
one can see, differences between the groups are still significant; thus, our results do not
change when the order of the continuous delay is moderately increased. However, differences
between the groups become smaller: the continuous delay group under-estimates the time it
takes to close the gap by 7.9 years (results for the discrete groups remain the same since
nothing was changed in the calculation of the estimation error for this group).
° See Roy (1999) for an estimation method for delay order when building system dynamics models. Furthermore,
Ozgun and Barlas (2009) have demonstrated how results of discrete and continuous simulation methods
approach each other when the number of items in a system is increased.
14
Table 4: Results of t-tests to check for differences between experimental groups: estimations
against actual target achievement—third-order delay system in continuous condition
Levene's Test for
Equality of Variances ttest for Equality of Means
Mean
F Sig. t df Sig. (2-tailed) Difference
ABSDeviati Equal variances
onCorrectE assumed 22.389 .000 | -4.308 45 000 -6.78000
stimate3rd
Equal variances
not assumed -4.189 | 34.622 .000 -6.78000
Thus, with regard to Proposition 3 we conclude that the participants with the discrete
delay condition do much better than the participants with the continuous delay condition
when it comes to estimating the effect of the delay. In other words, while both groups seem to
use the same cognitive representation to make their recommendation and estimate the target
year, this cognitive representation is much more appropriate in the discrete delay condition.
To substantiate this argument, we also compared the estimations of the continuous delay
group against a 20" order continuous delay. In this case, it takes approximately 14 years until
gender balance is achieved, given a 50% hiring of female professors. For this comparison, no
significant differences between the groups can be found anymore (although the estimations of
the discrete delay group are on average still better than the estimations of the continuous
group). In other words, the quality of the estimations of the two experimental groups can be
considered equally good, when we compare the estimations of the continuous delay group
against a higher-order delay that resembles a discrete (i.e. an infinite-order) delay.
Therefore, our preliminary finding is that people tend to cognitively represent delay as a
discrete delay conceptualisation, at least when performing a simple dynamic task on personnel
hiring, even in the case that the task rather explicitly refers to a continuous delay. Of course, if
the situation really involves a discrete delay, their performance is appropriate; however, if the
situation actually consists of a continuous delay, as many processes in human resource
management, a cognitive representation based on a discrete delay understanding can yield
only inferior results.
5. Conclusions and further research
In line with previous experiments in system dynamics and psychology, we find that people
have a general tendency to underestimate the effect of delays in dynamic systems. As such,
we can support our first proposition which is in line with existing research. However, our
15
major contribution to research is related to Proposition 2 and 3, stating that participants use a
comparable cognitive representation of delay, namely a discrete delay, in either tasks that refer
to a discrete and task that refer to a continuous delay.. It is important to point out that
representing delay as discrete is not necessarily an issue: in case the actual situation is
characterised by this type of delay, this is fine. However, problems occur when the actual
situation comprises continuous delays and not discrete delays, like for example in human
resource management and personnel hiring in particular.*
A general answer to the question ‘which form of delay better represents reality’ cannot
be given; it depends on the characteristics of the actual situation. Nevertheless, our results are
relevant since we would postulate that many issues that are subject to strategic decision-
making include continuous delays; rather than having a fixed and absolute delay time, many
such issues follow a stochastic, on-average form of behaviour For instance, in strategic
human resource management, hiring and training new employees takes a certain number of
months on average: there will always be personnel that can be recruited easily and that picks
up the necessary skills virtually immediately; they will finish their training long before the
average time. On the other hand, there will also be positions that can only hardly be filled or
people that take longer to understand the necessary knowledge; they will finish their training
(maybe even long) after the average time. The same continuous delay patterns must be
assumed for many other processes in strategic management: the development of new
products, the effectiveness of marketing activities, or, more general, the development of
strategic resources and capabilities. Our results suggest systematic problems when managers
have to make decisions on these processes based on their intuition; they might cognitively
represent delays as being discrete.
The results of this study are also interesting in terms of teaching system dynamics skills.
When educating future system dynamicists, we have experienced that the concept of
continuous delays is usually difficult to understand for novices. However, continuous delays
are the usual way to model non-instantaneous phenomena in system dynamics (for the reasons
outlined in the paragraph just above). Our study provides the warning that students of system
dynamics may frequently run into difficulties when initially introduced to the idea of
continuous delays: cognitively, they may be just better prepared to understand discrete delays.
Of course, the repetition of the experiment to achieve a higher number of participants
and to allow for a better differentiation between the two conditions conceming the task
* An assumption of why people generally might use discrete delay representations instead of continuous delay
representations would be that a discrete understanding of delays causes less cognitive load. However, what could
be evolutionary or other reasons for this phenomenon is outside our current understanding.
16
formulation are worthwhile ways to proceed with this research. One may argue that the results
of the task are context specific, since the task is politically loaded. However, the comparison
is done between two random selected groups that both experience this context. Nevertheless,
the test can be repeated to check if participants make a comparable estimation with a neutral
task.
This study reiterates the finding that people are not well-equipped to deal with dynamic
issues in general and delays in particular and sheds some additional light on how people
conceptualise delay structures. However, stating that people are just not very well capable to
deal with delays should of course not be the end of our endeavours. Rather, we want to
continue our research in order to improve (strategic) decision making. For example, decision
making tasks with delays can be re-designed in a way that allow “normal people” to
understand the dynamics caused by the delays and, thus, make successful decisions (Forrester,
1961). In other words, a practical implication of this study is the demand to find “nudges”
(Sawicka and Rydzak, 2007; cf. Thaler and Sunstein, 2008) that are necessary to improve
real-world decision making when delays are involved. However, our study makes clear that
this is not a trivial endeavour since participants even failed to understand delays correctly
when cues in the task were quite unequivocally favouring discrete or continuous delays.
Literature
Barlas, Y. and Ozevin, M. G. (2001). “Testing the Decision Rules Used in Stock Management
Models” Proceedings of the 19” International Conference of the System Dynamics
Society, Atlanta, GA. System Dynamics Society: Albany, NY.
Barlas, Y. and Ozevin, M. G. (2004). “Analysis of Stock Management Gaming Experiments
and Alternative Ordering Formulations” Systems Research and Behavioral Science
21(4): 439-470.
Bleijenbergh, I., Blonk, E., Schulte, L. and van Engen, M. (2008). “Explaining Women's
Careers at a Dutch university: Model building as a method for knowledge elicitation in
gender analysis” Proceedings of the 2008 International Conference of the System
Dynamics Society, Athens, Greece. System Dynamics Society: Albany, NY .
17
Bleijenbergh, I., Vennix, J., Jacobs, E. and Van Engen, M. (2011). “Reducing the Gender Gap:
biases in understanding delays in personnel policies” Working paper Radboud
University Nijmegen, January 2011.
Booth Sweeney, L. Sterman, J. D. (2000). “Bathtub Dynamics: Initial Results of a Systems
Thinking Inventory” System Dynamics Review 16(4): 249-286.
Brehmer, B. (1989). “Feedback Delays and Control in Complex Dynamic Systems”
Proceedings of the 1989 International System Dynamics Conference: Computer-Based
Management of Complex Systems, Stuttgart, Germany. System Dynamics Society:
Albany, NY.
Brehmer, B. (1990). “Strategies in Real-time, Dynamic Decision Making” In R. Hogarth
(Ed.): Insights in Decision Making, Chicago: University of Chicago Press.
Brehmer, B. (1992). “Dynamic Decision Making: Human Control of Complex Systems” Acta
Psychologica 81: 211-241.
Brehmer, B. (1995). “Feedback Delays in Complex Dynamic Decision Tasks” In P. A.
Frensch and J. Funke (Eds.): Complex Problem Solving — The European Perspective,
Hillsdale/Hove: Lawrence Erlbaum, 103-130.
Brehmer, B. and Allard, R. (1991). “Dynamic Decision Making: The Effects of Task
Complexity and Feedback Delay” In J. Rasmussen, B. Brehmer and J. Leplat (Eds.):
Distributed Decision Making: Cognitive Models of Cooperative Work, Chichester et al.:
John Wiley & Sons, 319-334.
Brehmer, B. and Domer, D. (1993). “Experiments with Computer-Simulated Microworlds:
Escaping Both the Narrow Straits of the Laboratory and the Deep Blue Sea of the Field
Study” Computers in Human Behavior 9: 171-184.
Cronin, M.A., Gonzalez, C., Sterman, J. D. (2009). “Why Don’t Well-Educated A dults
Understand Accumulation? A challenge to researchers, educators and citizens”
Organizational Behavior and Human Decision Processes 108: 116-130.
18
Diehl, E. W. (1989). “A Study on Human Control in Stock- Adjustment Tasks” Proceedings of
the 1989 International System Dynamics Conference: Computer-Based Management of
Complex Systems. Stuttgart, Germany. System Dynamics Society: Albany, NY.
Diehl, E. W. and Sterman, J. D. (1995). “Effects of Feedback Complexity on Dynamic
Decision Making” Organizational Behavior and Human Decision Processes 62(2): 198—
215.
Forrester, J. W. (1961). Industrial Dynamics. MIT Press: Cambridge, MA.
Frensch, P. A. and Funke, J. (Eds.)(1995). Complex Problem Solving — The European
Perspective, Hillsdale/Hove: Lawrence Erlbaum.
Funke, J. (1985). “Steuerung dynamischer Systeme durch den Aufbau und Anwendung
subjektiver Kausalmodelle” [Control of dynamic systems by development and
application of subjective causal models] Zeitschrift fiir Psychologie 193(4): 443-465.
Grofler, A. and A. Zock (2010). “Supporting Long-term Workforce Planning with a Dynamic
Aging Chain Model — a case study from the service industry” Human Resource
Management 49(5): 829-848.
Langley, P.A., Paich, M. and Sterman, J. D. (1998). “Explaining Capacity Overshoot and
Price Wars: Misperceptions of Feedback in Competitive Growth Markets” Proceedings
of the 16" International Conference of the System Dynamics Society, Quebec City,
Canada. System Dynamics Society: Albany, NY.
Matern, B. (1979). “Verzégertes Wirksamwerden von Eingriffen in der automatisierten
Industrie — Konsequenzen fiir die Arbeitsgestaltung” [Delayed Effects of Interventions
in the Automated Industry — consequences for the layout of work ] Sozialistische
Arbeitswissenschaft 23: 224-228.
19
Ossimitz, G. (2002). “Stock-Flow-Thinking and Reading Stock-Flow-Related Graphs: an
empirical investigation in dynamic thinking abilities” Proceedings of the 20%
International Conference of the System Dynamics Society, Palermo, Italy. System
Dynamics Society: Albany, NY.
Ozgun, O. and Barlas, Y . (2009). “Discrete vs. Continuous Simulation: When Does It
Matter?” The 27" Intemational Conference of the System Dynamics Society,
Albuquerque, NM. System Dynamics Society: Albany, NY.
Pala, ©. and Vennix, J. A. M. (2005). “Effect of System Dynamics Education on Systems
Thinking Inventory Task Performance” System Dynamics Review 21(2): 147-172.
Rahmandad H. (2008). “Effect of Delays on Complexity of Organizational Learning”
Management Science 54(7): 1297-1312.
Rahmandad, H., N. Repenning and J. D. Sterman (2009). “Effects of Feedback Delay on
Leaming” System Dynamics Review 25(4): 309-338.
Rahn, R. J. (1976). “Delays and Aggregation in System Dynamics Models” Proceedings of
the 1976 Intemational Conference on System Dynamics, Geilo, Norway. System
Dynamics Society: Albany, NY.
Reichert, U. and Domer, D. (1988). “Heurismen beim Umgang mit einem ‘einfachen’
dynamischen System” [Heuristics when Using a ‘Simple’ Dynamic System] Sprache &
Kognition 7: 12-24.
Repenning, N.P. and J. D. Sterman (2002). “Capability Traps and Self-Confirming A ttribution
Errors in the Dynamics of Process Improvement” Administrative Science Quarterly 47:
265-295.
Rouwette, E., A. GréBler and J. Vennix (2004). “Exploring Influencing Factors on
Rationality: a Literature Review of Dynamic Decision-Making Studies in System
Dynamics” Systems Research & Behavioral Science 21(4): 351-370.
20
Roy, R. K. (1999). “A Method for Estimating Order of System Dynamics Delays”
Proceedings of the 17" Intemational Conference of the System Dynamics Society and
5" Australian & New Zealand Systems Conference, Wellington, New Zealand. System
Dynamics Society: Albany, NY .
Roy, R. K. (2000). “Bulk Delays in System Dynamics Models” Proceedings of the 18”
International Conference of the System Dynamics Society, Bergen, Norway. System
Dynamics Society: Albany, NY.
Sawicka, A. and Rydzak, F. (2007). “Incorporating Delays in the Decision-Making Interface:
An Experimental Study” Proceedings of the 2007 Intemational Conference of the
System Dynamics Society, Boston, MA. System Dynamics Society: Albany, NY.
Sterman, J. D. (1989). “Misperceptions of Feedback in Dynamic Decision Making”
Organizational Behavior and Human Decision Processes 43: 301-335.
Sterman, J. D. (2010). “Does Formal System Dynamics Training Improve People’s
Understanding of Accumulation?” System Dynamics Review 26(4): 316-334.
Sterman, J. D. and Booth Sweeney, L. (2002). “Cloudy Skies: assessing public understanding
of global warming” System Dynamics Review 18(2): 207-240.
Stemberg, R. J. and Frensch, P. A. (Eds.)(1991). Complex Problem Solving — Principles and
Mechanisms, Hillsdale/Hove/London: Lawrence Enbaum
Sweeney, L. B. and J. D. Sterman (2000). “Bathtub Dynamics: Initial Results of a Systems
Thinking Inventory” System Dynamics Review 16(4): 249-286.
Thaler. R. H. and Sunstein, C. R. (2008). Nudge — Improving Decisions about Health, Wealth,
and Happiness. Yale University Press: Yale.
Yasarcan, H. (2011). “Stock Management in the Presence of Significant Measurement
Delays“ System Dynamics Review 27(1): 91-109.
21
Yasarcan, H. and Y. Barlas (2005). “A Generalized Stock Control Formulation for Stock
Management Problems Involving Composite Delays and Secondary Stocks” System
Dynamics Review 21(1): 33-68.
22
Appendix
Female Professors task — discrete delay condition
Experiment “Appointment of female professors”
The Board of a university has decided to drastically increase the number of female full
professors. The target is to have 50% female full professors at the university in the long run.
Currently, the percentage of female full professors is 11%. For 15 years already, the
percentage of female students is around 50% while 45% of the current PhD students are
female. It is expected that this percentage will increase in the years to come. This situation has
lead to the target being set at 50% for female full professors. Considering the financial
situation at institutions for higher education the assumption is that the number of full
professor positions will not increase. The change therefore has to occur within the current
number of full professor positions.
Currently, the number of positions for full professors at the university is 300. As stated, it is
expected that this number will not change in the future. In 2010, there are 33 female and 267
male full professors. As a simplification, we assume that a full professor position is held for
exacily 10 years (thus, all professors stay exactly the same period of time). After this period,
the professor retires or accepts a position at another university, so a new professor can be
appointed at that position. As mentioned, the target is to have 50% female full professors at
the university.
Within the Board there has been a long discussion about the strategy that has to be pursued to
achieve this target and the Board is convinced they have to implement a quota. This means
that faculties will be forced, as of 2010, to annually appoint a certain percentage of women on
vacant professor positions.
The Board asks your advice about how high this percentage should be and when you think the
target (of 50% female and 50% male professors) will be achieved.
23
My advice on annual percentage of female appointments:.........%
Using this percentage the target will be achieved by the year 20....
Could you please briefly explain your choices below?
Finally we would like to ask you a couple of additional questions.
Gender: man/woman
Y ear of birth: 19..
Study:
Thanks for your particpation!
24
Female Professors task — continuous delay condition
Experiment “Appointment of female professors”
The Board of a university has decided to drastically increase the number of female full
professors. The target is to have 50% female full professors at the university in the long run.
Currently, the percentage of female full professors is 11%. For 15 years already, the
percentage of female students is around 50% while 45% of the current PhD students are
female. It is expected that this percentage will increase in the years to come. This situation has
lead to the target being set at 50% for female full professors. Considering the financial
situation at institutions for higher education the assumption is that the number of full
professor positions will not increase. The change therefore has to occur within the current
number of full professor positions.
Currently, the number of positions for full professors at the university is 300. As stated, it is
expected that this number will not change in the future. In 2010, there are 33 female and 267
male full professors. On average, a full professor position is held for 10 years. This means
that some professors may stay for only a couple of years and then move on to another
university, while others may stay at this university for the rest of their career. From the
available data one can however conclude that the average length of stay of a full professor is
10 years. Only after a professor leaves, a new professor can be appointed at that position. As
mentioned, the target is to have 50% female full professors at the university.
Within the Board there has been a long discussion about the strategy that has to be pursued to
achieve this target and the Board is convinced they have to implement a quota. This means
that faculties will be forced, as of 2010, to annually appoint a certain percentage of women on
vacant professor positions.
The Board asks your advice about how high this percentage should be and when you think the
target (of 50% female and 50% male professors) will be achieved.
25
My advice on annual percentage of female appointments:.........%
Using this percentage the target will be achieved by the year 20....
Could you please briefly explain your choices below?
Finally we would like to ask you a couple of additional questions.
Gender: man/woman
Y ear of birth: 19..
Study:
Thanks for your particpation!
26
System dynamics model: Female Professors task — discrete delay condition
Female professors=INTEG (hiring women-leaving women, Ini Female);
Units: persons
FINAL TIME=100; Units: Year
hiring women=percentage women*hirings necessary; Units: persons/Year
hiring men=(l-percentage women) *hirings necessary; Units:
persons/Year
hirings necessary=leaving women+leaving men; Units: persons/Year
Ini Female=33; Units: persons
Ini Male=267; Units: persons
INITIAL TIME=0; Units: Year
leaving women=DELAY FIXED (hiring women, time at university, Ini
Female/time at university); Units: persons/Year
leaving men=DELAY FIXED (hiring men, time at university, Ini
Male/time at university); Units: persons/Year
Male professors=INTEG (hiring men-leaving men, Ini Male); Units:
persons
percentage women=0.5; Units: Dmnl
time at university=10; Units: Year
TIME STEP=1; Units: Year
System dynamics model: Female Professors task — continuous delay condition (1* order
delay; only differences to discrete delay model shown)
leaving women=Female professors/time at university; Units:
persons/Year
leaving men=Male professors/time at university; Units: persons/Year
27
